The Butler family drives home from a vacation. The table of values that follows shows the relationship between the number of gallons, g, of gasoline their car uses and the distance in miles, d, the car is from home:


Gallons of Gasoline Used (g) Distance from Home (d)
1 144
2 124
3 104
4 84
5 64

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I intuit you are looking for

d(g) = 164-20g

To find the relationship between the number of gallons (g) of gasoline used and the distance from home (d), we can plot these points on a graph and look for any patterns or trends.

Let's start by plotting the points on a graph:

Gallons of Gasoline Used (g) Distance from Home (d)
1 144
2 124
3 104
4 84
5 64

Now, we can plot these points on a graph with the x-axis representing the gallons of gasoline used (g) and the y-axis representing the distance from home (d).

After plotting the points, we can see that as the number of gallons of gasoline used decreases, the distance from home also decreases. This indicates an inverse relationship between the number of gallons of gasoline used and the distance from home.

To find the equation that represents this relationship, we can use the method of least squares to fit a line to the data points. This line will represent the best approximation of the relationship between the variables.

Using a graphing calculator or a statistical software, we can input these data points and find the equation of the line of best fit. The resulting equation will give us the relationship between the number of gallons of gasoline used and the distance from home.

Once we have the equation, we can use it to find the distance from home for any given number of gallons of gasoline used.